Step by step
The question
Question: Data: 2, 4, 6, 20.
Remove 20.
What happens to the mean and the median?
1 Mean before
We add all the numbers, from left to right.
So the total is 32.
There are 4 numbers.
The mean shares the total equally: 32 divided by 4.
So the mean is 8.
2 Median before
The median is the middle number.
For it, the numbers must be in order.
They already are, smallest first.
We cross out the smallest and the biggest, one pair at a time.
Two numbers are left in the middle: 4 and 6.
The median is halfway between them: we add them and divide by 2.
4 plus 6 is 10.
10 divided by 2 is 5.
3 Mean after
20 is gone, so the total loses 20.
32 minus 20 is 12.
One number less: now there are 3.
Careful!
We have 3 numbers now, not 4.
So we share by 3.
We share the new total equally: 12 divided by 3.
So the new mean is 4.
4 Median after
Now the list in order, without 20.
We cross out the smallest and the biggest, one pair at a time.
4 is left in the middle.
So the new median is 4.
5 Compare
The mean went down from 8 to 4.
8 minus 4 is 4.
So it went down 4.
The median went down from 5 to 4.
5 minus 4 is 1.
So it went down 1.
20 is far from the other numbers.
A far number pulls the mean a lot.
Only the middle numbers matter for the median.
So the far number does not pull it, and it moves just a little.
So the mean goes down 4, and the median goes down 1.
6 Check
Let's check the new mean: if every number were 4, 3 of them would make 4 times 3.
That is 12, the new total.
So it is right!
Let's look back.
First: mean before.
Then: median before.
Then: mean after.
Then: median after.
Then: compare.
Last: check.